Weir

WEIR CALCULATOR

Rectangular Sharp Crested Weir

Free discharge Drowned flow
  • Q = Discharge (flow rate).
  • Cd = Discharge coefficient
  • b = Width of rectangular weir
  • B = Width of channel
  • h1 = Upstream depth of water above weir
  • h2 = Downstream depth of water above weir
  • p1 = Upstream depth from weir crest to channel bed
  • p2 = Downstream depth from weir crest to channel bed
References

Fenton, J. D. (2015) Calculating flow over rectangular sharp-edged weirs, Alternative Hydraulics Paper 6, http://johndfenton.com/Papers/Calculating-flowover-rectangular-sharp-edged-weirs.pdf

Kindsvater, C. E. & Carter, R. W. C. (1957), Discharge characteristics of rectangular thin plate weirs, J. Hydraulics Div. ASCE 83(HY6), 1453/1–1453/36.

Triangular Sharp Crested Weir

Free discharge Drowned flow
  • Q = Discharge (flow rate).
  • C = Discharge coefficient
  • k = Head adjustment factor
  • \theta = Angle of v-notch
  • B = Width of channel
  • h1 = Upstream depth of water above v of weir
  • p1 = Upstream depth from weir v to channel bed
USBR (1997) suggests using the V-notch weir equations for the following conditions:
  • Head (h) should be measured at a distance of at least 4h upstream of the weir.
  • It doesn't matter how thick the weir is except where water flows over the weir through the "V." The weir should be between 0.03 and 0.08 inches (0.8 to 2 mm) thick in the V. If the bulk of the weir is thicker than 0.08 inch, the downstream edge of the V can be chamfered at an angle greater than 45o (60o is recommended) to achieve the desired thickness of the edges. You want to avoid having water cling to the downstream face of the weir.
  • Water surface downstream of the weir should be at least 0.2 ft. (6 cm) below the bottom of the V to allow a free flowing waterfall.
  • Measured head (h) should be greater than 0.2 ft. (6 cm) due to potential measurement error at such small heads and the fact that the nappe (waterfall) may cling to the weir.
  • The equations have been developed for h<1.25 ft. (38 cm) and h/P<2.4.
  • The equations have been developed for fully contracted V-notch weirs which means h/B should be ≤ 0.2.
  • The average width of the approach channel (B) should be > 3 ft. (91 cm).
  • The bottom of the "V" should be at least 1.5 ft. (45 cm) above the bottom of the upstream channel.
References

Shen, J. (1981). Discharge characteristics of triangular-notch thin-plate weirs. Studies of flow of water over weirs and dams. Geological Survey Water-Supply Paper 1617-B, Washington D. C.

USBR. (1997). U.S. Department of the Interior, Bureau of Reclamation. Water Measurement Manual. 3ed.

LMNO Engineering. V-Notch (Triangular) Weir Calculator. https://www.lmnoeng.com/Weirs/vweir.php

I want to find the of my

Cross Section Input

Weir Width (b) m
Channel Width (B) m
Upstream depth to crest (P1) m
Downstream depth to crest (P2) m
Downstream depth of water above weir (h2)
(leave blank for free discharge)
m

Cross Section Input

Bottom Angle °
Downstream depth of water above weir (h2)
(leave blank for free discharge)
m

Other Inputs

Upstream depth of water above weir (h1) m
Coefficient of discharge (optional)

Outputs

Coefficient of Discharge
Flow Discharge m³/s

Other Inputs

Flow Discharge m³/s
Coefficient of discharge (optional) m/m

Outputs

Coefficient of Discharge
Upstream depth of water above weir (h1) m